%I #10 Oct 08 2022 14:17:03

%S 1,1,3,15,105,923,9417,105815,1267681,15875631,205301361

%N Number of marked chord diagrams (linear words in which each letter appears twice) with n chords, whose intersection graph is distance-hereditary.

%C For n < 5, all intersection graphs on n vertices are distance-hereditary, so the first 4 terms coincide with the number of linear chord diagrams (given by the double factorial numbers; see A001147).

%H Christopher-Lloyd Simon, <a href="https://arxiv.org/abs/2106.15450">Topologie et dénombrement des courbes algébriques réelles</a>, arXiv:2106.15450 [math.AG], 2021.

%H Christopher-Lloyd Simon, <a href="https://doi.org/10.5802/afst.1698">Topologie et dénombrement des courbes algébriques réelles</a>, Annales de la faculté des sciences de Toulouse : Mathématiques, 6e série, 31(2): 383--422, 2022.

%F G.f. is algebraic: (z^3 + z^2)*A^6 - z^2*A^5 - 4*z*A^4 + (8*z + 2)*A^3 - (4*z + 6)*A^2 + 6*A - 2 = 0.

%Y Cf. A277862, A277869, A354588.

%K nonn,more

%O 0,3

%A _Christopher-Lloyd Simon_, Oct 05 2022